Get Equal Substrings Within Budget

The task is to find the maximum length of a substring of string s that can be changed to match the corresponding substring of string t with a cost less than or equal to maxCost. The cost of changing a character is defined as the absolute difference between the ASCII values of the characters.

Step-by-Step Approach

  1. Calculate Costs: Create an array costs where costs[i] represents the cost to change s[i] to t[i].
  2. Use Sliding Window Technique: Define a window that represents a valid substring of s that can be changed to t. If the total cost within the window exceeds maxCost, move the start of the window to the right.
  3. Maximize the Window Length: Continuously adjust the window to find the maximum length that satisfies the cost constraint.
  4. Return the Result: The maximum length of the window will be the answer.

Code

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class Solution:
    def equalSubstring(self, s: str, t: str, maxCost: int) -> int:
        # Step 1: Calculate the costs
        costs = [abs(ord(s[i]) - ord(t[i])) for i in range(len(s))]

        # Step 2: Initialize the sliding window
        start = 0
        totalCost = 0
        maxLength = 0

        # Step 3: Iterate through the string to adjust the window
        for end in range(len(s)):
            totalCost += costs[end]

            # If the cost exceeds maxCost, move the start of the window
            while totalCost > maxCost:
                totalCost -= costs[start]
                start += 1

            # Update the maximum length
            maxLength = max(maxLength, end - start + 1)

        # Step 4: Return the result
        return maxLength

Complexity Analysis

The time complexity of this code is (O(n)), where (n) is the length of the strings s and t, as it iterates through the strings once. The space complexity is (O(n)) due to the costs array.

Insights and Key Takeaways

  • The problem is efficiently solved using the sliding window technique.
  • The window represents a valid substring that can be changed, and its size is adjusted according to the costs.
  • By understanding the cost constraint and character relationships, we can apply the sliding window method to identify the longest valid substring quickly.
  • This solution adheres to the constraints and requirements of the problem.